Gateways Unveiling The Mysteries Of Topological Graph Theory
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Gateways Unveiling The Mysteries Of Topological Graph Theory
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-03-09
Gateways Unveiling The Mysteries Of Topological Graph Theory written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-09 with Mathematics categories.
Embark on a captivating journey through the world of topological graph theory, a captivating field that unveils the profound interplay between topology and graph theory. This comprehensive and engaging book offers a comprehensive exposition of the fundamental concepts, diverse applications, and recent advancements in topological graph theory, catering to a wide audience of mathematicians, computer scientists, and anyone fascinated by the intricate world of graphs and surfaces. Unravel the mysteries of graph imbeddings, delving into the intricate connections between graphs and surfaces. Explore the concept of genus, a captivating measure of the complexity of graph imbeddings, and uncover the profound implications of Ringel-Youngs theorem, a groundbreaking result that revolutionized the field of graph theory. Discover the wide-ranging applications of topological graph theory, spanning diverse fields such as computer science, network analysis, physics, and biology. Learn how topological graph theory empowers us to solve complex problems in network design, data analysis, and scientific modeling. Navigate through a wealth of captivating examples, illuminating figures, and thought-provoking exercises, all carefully crafted to enhance your understanding and deepen your appreciation for topological graph theory. Engage with the cutting-edge research and unsolved problems at the forefront of topological graph theory, gaining insights into the future directions and open challenges in this captivating field. Written with clarity and rigor, this book serves as an indispensable resource for mathematicians, computer scientists, and anyone seeking to delve into the captivating realm of topological graph theory. Whether you are a seasoned researcher, a budding student, or simply a curious explorer of the intricate world of graphs and networks, this book promises an enlightening and intellectually stimulating experience. If you like this book, write a review!
Topics In Topological Graph Theory
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Author : Lowell W. Beineke
language : en
Publisher: Cambridge University Press
Release Date : 2009-07-09
Topics In Topological Graph Theory written by Lowell W. Beineke and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-09 with Mathematics categories.
The use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature. Other books cover portions of the material here, but there are no other books with such a wide scope. This book contains fifteen expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory and the topology of surfaces. Each chapter concludes with an extensive list of references.
Topological Graph Theory
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Author : Jonathan L. Gross
language : en
Publisher: Courier Corporation
Release Date : 2001-01-01
Topological Graph Theory written by Jonathan L. Gross and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
Iintroductory treatment emphasizes graph imbedding but also covers connections between topological graph theory and other areas of mathematics. Authors explore the role of voltage graphs in the derivation of genus formulas, explain the Ringel-Youngs theorem, and examine the genus of a group, including imbeddings of Cayley graphs. Many figures. 1987 edition.
The Foundations Of Topological Graph Theory
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Author : C.Paul Bonnington
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Foundations Of Topological Graph Theory written by C.Paul Bonnington and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This is not a traditional work on topological graph theory. No current graph or voltage graph adorns its pages. Its readers will not compute the genus (orientable or non-orientable) of a single non-planar graph. Their muscles will not flex under the strain of lifting walks from base graphs to derived graphs. What is it, then? It is an attempt to place topological graph theory on a purely combinatorial yet rigorous footing. The vehicle chosen for this purpose is the con cept of a 3-graph, which is a combinatorial generalisation of an imbedding. These properly edge-coloured cubic graphs are used to classify surfaces, to generalise the Jordan curve theorem, and to prove Mac Lane's characterisation of planar graphs. Thus they playa central role in this book, but it is not being suggested that they are necessarily the most effective tool in areas of topological graph theory not dealt with in this volume. Fruitful though 3-graphs have been for our investigations, other jewels must be examined with a different lens. The sole requirement for understanding the logical development in this book is some elementary knowledge of vector spaces over the field Z2 of residue classes modulo 2. Groups are occasionally mentioned, but no expertise in group theory is required. The treatment will be appreciated best, however, by readers acquainted with topology. A modicum of topology is required in order to comprehend much of the motivation we supply for some of the concepts introduced.
Topological Theory Of Graphs
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Author : Yanpei Liu
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-03-06
Topological Theory Of Graphs written by Yanpei Liu and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-06 with Mathematics categories.
This book presents a topological approach to combinatorial configurations, in particular graphs, by introducing a new pair of homology and cohomology via polyhedra. On this basis, a number of problems are solved using a new approach, such as the embeddability of a graph on a surface (orientable and nonorientable) with given genus, the Gauss crossing conjecture, the graphicness and cographicness of a matroid, and so forth. Notably, the specific case of embeddability on a surface of genus zero leads to a number of corollaries, including the theorems of Lefschetz (on double coverings), of MacLane (on cycle bases), and of Whitney (on duality) for planarity. Relevant problems include the Jordan axiom in polyhedral forms, efficient methods for extremality and for recognizing a variety of embeddings (including rectilinear layouts in VLSI), and pan-polynomials, including those of Jones, Kauffman (on knots), and Tutte (on graphs), among others. Contents Preliminaries Polyhedra Surfaces Homology on Polyhedra Polyhedra on the Sphere Automorphisms of a Polyhedron Gauss Crossing Sequences Cohomology on Graphs Embeddability on Surfaces Embeddings on Sphere Orthogonality on Surfaces Net Embeddings Extremality on Surfaces Matroidal Graphicness Knot Polynomials
Topological Graph Theory
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Author :
language : en
Publisher:
Release Date : 2005
Topological Graph Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Thirty Essays On Geometric Graph Theory
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Author : János Pach
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-15
Thirty Essays On Geometric Graph Theory written by János Pach and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-15 with Mathematics categories.
In many applications of graph theory, graphs are regarded as geometric objects drawn in the plane or in some other surface. The traditional methods of "abstract" graph theory are often incapable of providing satisfactory answers to questions arising in such applications. In the past couple of decades, many powerful new combinatorial and topological techniques have been developed to tackle these problems. Today geometric graph theory is a burgeoning field with many striking results and appealing open questions. This contributed volume contains thirty original survey and research papers on important recent developments in geometric graph theory. The contributions were thoroughly reviewed and written by excellent researchers in this field.
Topological Graph Theory
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Author : Caryl Ann Chacey
language : en
Publisher:
Release Date : 1976
Topological Graph Theory written by Caryl Ann Chacey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Graph theory categories.
Special Issue Topological Graph Theory
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Author : Bojan Mohar
language : en
Publisher:
Release Date : 2004
Special Issue Topological Graph Theory written by Bojan Mohar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Graphs On Surfaces
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Author : Joanna A. Ellis-Monaghan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-28
Graphs On Surfaces written by Joanna A. Ellis-Monaghan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-28 with Mathematics categories.
Graphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications. The authors illustrate the interdependency between duality, medial graphs and knots; how this interdependency is reflected in algebraic invariants of graphs and knots; and how it can be exploited to solve problems in graph and knot theory. Taking a constructive approach, the authors emphasize how generalized duals and related ideas arise by localizing classical constructions, such as geometric duals and Tait graphs, and then removing artificial restrictions in these constructions to obtain full extensions of them to embedded graphs. The authors demonstrate the benefits of these generalizations to embedded graphs in chapters describing their applications to graph polynomials and knots. Graphs on Surfaces: Dualities, Polynomials, and Knots also provides a self-contained introduction to graphs on surfaces, generalized duals, topological graph polynomials, and knot polynomials that is accessible both to graph theorists and to knot theorists. Directed at those with some familiarity with basic graph theory and knot theory, this book is appropriate for graduate students and researchers in either area. Because the area is advancing so rapidly, the authors give a comprehensive overview of the topic and include a robust bibliography, aiming to provide the reader with the necessary foundations to stay abreast of the field. The reader will come away from the text convinced of advantages of considering these higher genus analogues of constructions of plane and abstract graphs, and with a good understanding of how they arise.